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Find the area of a triangle whose sides ...

Find the area of a triangle whose sides are 20 cm, 34 cm and 42 cm. Hence find the height corresponding to the longest side.

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Let a = 20 cm , b = 34 cm and c = 42 cm
`:. " " s=(a+b+c)/(2)=(20+34+42)/(2)=48 cm`
`:. " " ` Area `=sqrt(s(s-a)(s-b)(s-c))`
`=sqrt(48(48-20)(48-34)(48-42))`
`=sqrt(48xx28xx14xx6)`
`=336 " cm"^(2)`
Here, the longest side = 42 cm.
Let the corresponding height = h cm.
`:.` Area of triangle `=(1)/(2) xx"base" xx"height"`
or `336=(1)/(2)xx42xxh`
`rArr " " h=16` cm.
`:.` Height corresponding to longest side = 16 cm.
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